Asymptotic behavior and non-existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group

E. Lanconelli; F. Uguzzoni

Bollettino dell'Unione Matematica Italiana (1998)

  • Volume: 1-B, Issue: 1, page 139-168
  • ISSN: 0392-4041

How to cite

top

Lanconelli, E., and Uguzzoni, F.. "Asymptotic behavior and non-existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group." Bollettino dell'Unione Matematica Italiana 1-B.1 (1998): 139-168. <http://eudml.org/doc/195874>.

@article{Lanconelli1998,
author = {Lanconelli, E., Uguzzoni, F.},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {asymptotic behavior; semilinear boundary value problem; Heisenberg group; Sobolev space},
language = {eng},
month = {2},
number = {1},
pages = {139-168},
publisher = {Unione Matematica Italiana},
title = {Asymptotic behavior and non-existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group},
url = {http://eudml.org/doc/195874},
volume = {1-B},
year = {1998},
}

TY - JOUR
AU - Lanconelli, E.
AU - Uguzzoni, F.
TI - Asymptotic behavior and non-existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group
JO - Bollettino dell'Unione Matematica Italiana
DA - 1998/2//
PB - Unione Matematica Italiana
VL - 1-B
IS - 1
SP - 139
EP - 168
LA - eng
KW - asymptotic behavior; semilinear boundary value problem; Heisenberg group; Sobolev space
UR - http://eudml.org/doc/195874
ER -

References

top
  1. BAHRI, A.- CORON, J. M., On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math., 41 (1988), 253-294. Zbl0649.35033MR929280
  2. BENCI, V.- CERAMI, G., Existence of positive solutions of the equation - Δ u + a x u = u N + 2 / N - 2 in R N , J. Funct. Anal., 88 (1990), 90-117. Zbl0705.35042MR1033915
  3. BIRINDELLI, I.- CAPUZZO DOLCETTA, I.- CUTRÌ, A., Liouville theorems for semilinear equations on the Heisenberg group, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear. Zbl0876.35033MR1450950
  4. BREZIS, H.- KATO, T., Remarks on the Schrödinger operator with singular complex potentials, J. Math. Pures Appl., 58 (1979), 137-151. Zbl0408.35025MR539217
  5. BREZIS, H.- NIRENBERG, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477. Zbl0541.35029MR709644
  6. BURGER, N., Espace des fonctions à variation moyenne bornée sur un espace de nature homogène, C. R. Acad. Sci. Paris, Serie A, 286 (1978), 139-142. Zbl0368.46037MR467176
  7. CITTI, G., Semilinear Dirichlet problem involving critical exponent for the Kohn Laplacian, Ann. Mat. Pura Appl., 169 (1995), 375-392. Zbl0848.35040MR1378482
  8. CITTI, G.- GAROFALO, N.- LANCONELLI, E., Harnack's inequality for sum of squares of vector fields plus a potential, Amer. J. Math., 115 (1993), 699-734. Zbl0795.35018MR1221840
  9. CYGAN, J., Wiener's test for the Brownian motion on the Heisenberg group, Colloquium Math., 39 (1978), 367-373. Zbl0409.60075MR522380
  10. ESTEBAN, M. J.- LIONS, P.-L., Existence and non-existence results for semilinear elliptic problems in unbounded domains, Proc. Royal Soc. Edinburgh, 93A (1982), 1-14. Zbl0506.35035MR688279
  11. FEDERER, H., Geometric Measure Theory, Die Grundlehren der mathematischen Wissenschaften, 153, Springer, New York (1969). Zbl0176.00801MR257325
  12. FOLLAND, G. B., A fundamental solution for a subelliptic operator, Bull. Amer. Math. Soc., 79 (1973), 373-376. Zbl0256.35020MR315267
  13. FOLLAND, G. B.- STEIN, E. M., Estimates for the ¯ b complex and analysis on the Heisenberg group, Comm. Pure Appl. Math., 27 (1974), 429-522. Zbl0293.35012MR367477
  14. GAROFALO, N.- LANCONELLI, E., Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation, Ann. Inst. Fourier Grenoble, 40 (1990), 313-356. Zbl0694.22003MR1070830
  15. GAROFALO, N.- LANCONELLI, E., Existence and nonexistence results for semilinear equations on the Heisenberg group, Indiana Univ. Math. J., 41 (1992), 71-98. Zbl0793.35037MR1160903
  16. GILBARG, D.- TRUDINGER, N. S., Elliptic partial differential equations of second order, Die Grundlehren der mathematischen Wissenschaften, 224, Springer-Verlag, New York (1977). Zbl0361.35003MR473443
  17. JERISON, D. S., The Dirichlet problem for the Kohn Laplacian on the Heisenberg group I, J. Funct. Anal., 43 (1981), 97-142. Zbl0493.58021MR639800
  18. JERISON, D.- LEE, J. M., Intrinsic CR normal coordinates and the CR Yamabe problem, J. Differential Geom., 29 (1989), 303-343. Zbl0671.32016MR982177
  19. JERISON, D.- LEE, J. M., Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem, J. Amer. Math. Soc., 1 (1988), 1-13. Zbl0634.32016MR924699
  20. KOHN, J. J.- NIRENBERG, L., Non-coercive boundary value problems, Comm. Pure Appl. Math., 18 (1965), 443-492. Zbl0125.33302MR181815
  21. LIONS, P-L., The concentration-compactness principle in the calculus of variations. The limit case, Rev. Mat. Iberoamericana, 1 (1985), n. 1, 145-201, n. 2, 45-121. Zbl0704.49005MR850686
  22. TALENTI, G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl., Serie IV, 110 (1976), 353-372. Zbl0353.46018MR463908
  23. UGUZZONI, F., A Liouville-type theorem on halfspaces for the Kohn Laplacian, Proc. Amer. Math. Soc., to appear. Zbl0907.31006MR1458268

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.